CMOS Position-Based Charge Qubits: Theoretical Analysis of Control and Entanglement

Abstract

In this study, a formal definition, robustness analysis and discussion on the control of a position-based semiconductor charge qubit are presented. Such a qubit can be realized in a chain of coupled quantum dots, forming a register of charge-coupled transistor-like devices, and is intended for CMOS implementation in scalable quantum computers. We discuss the construction and operation of this qubit, its Bloch sphere, and relation with maximally localized Wannier functions which define its positionbased nature. We then demonstrate how to build a tight-binding model of single and multiple interacting qubits from first principles of the Schrödinger formalism. We provide all required formulae to calculate the maximally localized functions and the entries of the Hamiltonian matrix in the presence of interaction between qubits. We use three illustrative examples to demonstrate the electrostatic interaction of electrons and discuss how to build a model for many-electron (qubit) system. To conclude this study, we show that charge qubits can be entangled through electrostatic interaction.INDEX TERMS CMOS technology, charge qubit, position-based qubit, electrostatically controlled qubit, single-electron devices, tight-binding formalism, Schrödinger formalism, entanglement, entanglement entropy, Bloch sphere.2

A Fully Integrated DAC for CMOS Position-Based Charge Qubits with Single-Electron Detector Loopback Testing

“…Fig. 1 presents an overview of the CMOS position-based charge qubit structure containing an array of QDs [9], [11], [12], with schematics of nearby interfacing circuitry: reset, control, singleelectron injector, and detector. It is part of a quantum processor implemented in 22-nm FDSOI CMOS and operating at cryogenic temperature of 3.4 K, whose earlier version was presented in [10].…”

“…Table I summarizes the key specifications for the CDAC in the proposed system. The values are derived from physical equations and COMSOL multiphysics modeling of the QDA structures [9], [11]. To overcome the kT/q thermal energy of an electron, the LSB voltage step (i.e., resolution) at the tunnel junction between QDs should be finer than 300 µV at 4 K. However, the voltage applied at the imposer gates should be ∼10× larger due to the capacitive division between C ox (gate oxide capacitance) and C t (tunnel junction capacitance).…”

“…This demands the massive scalability in the number of qubits [3]- [5], but it poses main bottlenecks in the growing number of I/O signals for off-chip control electronics, as well as I/O congestion and system complexity [1], [6], [7]. To address this scaling problem, CMOS technology has been recently investigated for constructing spin [8] and position-based charge [9] qubits, which will naturally allow them to be monolithically integrated with their control, stimulus, and readout circuitry.…”

“…Our proposed quantum processor unit (QPU) uses on-chip interface circuitry to electrostatically set the quantum states of position-based charge qubits in accordance with a given quantum algorithm [9]- [12]. These proposed quantum states are controlled by adjusting potential barriers between quantum dots (QDs) to establish, via tunneling and entanglement, the intended functions of quantum gates.…”

“…In contrast with the spin-based qubit interfaces that require wide bandwidth circuitry operating at microwaves [4], the charge-based qubits can be electrostatically interfaced with baseband pulses [10], [12]. Furthermore, although the charge qubits are known to suffer from the relatively short decoherence time (50 ns to 1 µs), the ultra-high transition frequency f T in advanced CMOS can help to fit over a thousand quantum gate operations within the useful decoherence duration [9].…”